Full Idea
The Principle of Thinning says that if a set of premisses entails a conclusion, then adding further premisses will still entail the conclusion. It is 'thinning' because it makes a weaker claim. If γ|=φ then γ,ψ|= φ.
Gist of Idea
'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference
Source
David Bostock (Intermediate Logic [1997], 2.5.B)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.30
A Reaction
It is also called 'premise-packing'. It is the characteristic of a 'monotonic' logic - where once something is proved, it stays proved, whatever else is introduced.